The author has been investigated the structural design method of frames composed of core steel composite columns and reinforced concrete beams (RC beam). In general reinforced main bars of RC beam are arranged densely at the beam-to column connection panel, so encasing core steel of column member through into beam connection is difficult. As one of method of making clear up the difficulty, cutting and encasing core steel out of beam-to-column connection can be thought. In order to study the elastic-plastic behavior of cruciform frames composed of core steel composite columns and reinforced concrete beams, an experimental work was carried out. In order to make clear the behavior of frames under large axial load, the axial load of column was applied 0.4 times of ultimate compressive strength of column cross section. Experimental parameter is different of encasing core steel into column members, (1) cutting core steel at the connection panel and no reinforcement of core steel (A-Type), (2) cutting core steel at theconnection panel and welding of steel plate at the end of core steel in order to prevent bearing collapse of concrete of beam-to-column connection (B-Type), and (3) encasing core steel through into connection panel (C-Type).It was clear by carrying out the experimental work that : Specimen of C-Type showed stable behavior up to the story drift R =4/100 rad. Specimen of B-Type showed almost same behavior up to the story drift R=2.5/100, and the axial compressive load of core steel of this specimen kept 1.5 times of one of A-Type specimen. Under the large axial load on the column, welding of steel plate at the end of core steel is useful on the point of reinforcing at the connection panel.